Failure of the Pooling Equilibrium:

Although in Figure, A satisfies one of the equilibrium conditions,  i.e., the breaks even condition by  virtue of its being on the aggregate fair odds line, it fails in case of another. See that no potentially competing contract can make a non-negative  profit.  For  example, if another insurance company  offers  a policy  like point B  in  the  figure, types H will not be  the gainers. As B  lies strictly below UH,  SO H types are happier with the current policy.

However, consider L types. They strictly prefer this policy as B  is above UL. Since B  lies above the fair odds line for  the pooling policy  it offers a better deal to this group. However, it fails to provide much insurance as it lies closer to  E  than  that of A. T subsidising the H types. It is clear that for the opposite reasons, H  types would prefer the old policy.  So, when policy B is offered, all L  types change  to B, and the H  types stick with A. Because B  lies below  the fairs odds line for L types  it  is profitable  if  it attracts L types. But A cannot be offered without the L types participating as it requires the cross-subsidy.

Consequently, the pooling equilibrium cannot exist. It is always undermined by a 'separating' policy that skims off the L types from the pool. See  that the insurer enters into a process whereby it tries to select the most favourable individuals with expected losses below the premium charged. Free entry leads to 'cream  skimming'  of  low-risk from  the pool and makes  it difficult or impossible for  individuals with high expected losses to purchase private insurance. This causes pooling policy to lose money because only high risk remains and pooling policy disappears.

In  above  result we see how  it makes  sense  to  separate  the  profitable group from that  of  the  less profitable  one. If an insurance company loses money on one group but makes it back on another, there is a strong incentive to separate the profitable from the unprofitable group and charge them different prices or just  drop the unprofitable group, thereby undermining the cross-subsidy.